Application of asymptotic iteration method to a deformed well problem

The asymptotic iteration method (AIM) is used to obtain the quasi-exact solutions of the Schrödinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.